WASHINGTON — Speaker John Boehner and House Republicans did not produce any new strategy Friday to end the government shutdown that entered its fifth day Saturday, while keeping up a barrage aimed at shifting blame to Democrats.

“This isn’t some damn game!” Boehner declared at a press conference during which he exhorted President Obama and Senate majority leader Harry Reid to negotiate a funding bill that would reopen government.

There was no movement by either side, and no negotiations were pending. There was plenty of speculation in the Capitol that Boehner was considering various plans to deal with both the shutdown and the next potential crisis point, the need to raise the national debt limit before Oct. 17.

Boehner was widely reported to have told colleagues on Thursday that he would be willing to pass a debt-limit increase with a coalition of Democrats and Republicans, but that, too, has not been confirmed publicly or spelled out. On Friday, the message returned to one of party solidarity.

Representative John Fleming, an Arkansas Republican, said Boehner did not discuss any deals during the morning meeting and said, “He has no intention of rolling over on anything.”

Instead, House Republicans continued its efforts to reverse-engineer the government shutdown with more attempts to restore funding to select, high-profile programs and services through piecemeal bills. The Democratic-controlled Senate has said it will reject such partial measures.

“Small steps start a long journey, and we have a long journey to go.”

Representative Jack Kingston, Republican from Georgia

As a storm churns in the Gulf of Mexico, the Federal Emergency Management Agency and the National Weather Service were on the House docket Friday to receive funding. So was the food and nutrition program for low-income women and children.

On Saturday, the House is scheduled to meet to vote on bills that would restore the salaries of all furloughed federal employees once the government reopens. Next week it will consider a bill that would finance Head Start, preschool for children from low-income families.

“Getting some of the agreeable things done up front gives you momentum,” said Jack Kingston, a Georgia Republican. “At least little slivers get you moving. Small steps start a long journey, and we have a long journey to go.”

Democrats called the slew of bills a political stunt and “cynical ploy” to deflect blame for the shutdown, which began Tuesday after Republicans refused to back down from their demands that a government funding bill also dismantle, delay, or weaken President Obama’s new health care insurance expansion.

Senate majority whip Dick Durbin, an Illinois Democrat, joked about a strategy to get Republicans to end the shutdown, citing all the exceptions the Tea Party has agreed to fund.

“Maybe we should go to the floor of the Senate or the House and read the directory of all the federal agencies,” Durbin said. “Would they open the government then?”

Representative Jim McGovern, a Massachusetts Democrat, said he took particular insult at what he characterized as Republicans’ sudden concern about poverty and hunger after they spent months trying to slash tens of billions from food assistance programs.

“Republicans would like us all to believe that they care about hunger in America,” McGovern said on the House floor. “Give me a break, Mr. Speaker. Where have you been?”

The House has already passed bills to re-open parks and memorials, fund veterans services, and the National Institutes of Health. The White House has made it clear it would veto bills that restore funding to limited activities.

But on Friday the Obama administration said it supports the passage of the bipartisan House bill to retroactively compensate furloughed employees.

“This bill alone, however, will not address the serious consequences of the funding lapse, nor will a piecemeal approach to appropriations bills,” said a statement issued by the Office of Management and Budget. The White House had also supported an earlier bill to pay members of the military.

“So, to recap, the President signed the troop funding bill, and does not oppose back pay, but he has promised to veto bills helping veterans, cancer research, National Parks, the District of Columbia,” said Boehner spokesman Michael Steel. “Interesting priorities.”

Obama, who canceled a trip to Indonesia and Brunei because of the shutdown, said on Friday that the shutdown could end immediately if Boehner would schedule a vote on a bill to pay for government operations through Nov. 15, which the Senate has already passed.

“I’m happy to have negotiations but we can’t do it with a gun held to the head of the American people,” Obama told reporters during a stop at a sandwich shop near the White House for lunch with Vice President Joe Biden.

While close to two dozen mainstream conservative Republicans are reportedly ready to support a “clean” bill to fund the government that would not attempt to change Obama’s health care law, the Tea Party faction still refuses to budge.

“We’re not tweaking any strategy,” said Fleming, the representative from Arkansas.

“I don’t think that many of my constituents even know that there’s a shutdown, or really care,” Fleming said.

He conducted a tele-townhall with his constituents Thursday night, and he said, “All they wanted to talk about was the dreaded Obamacare and the fact that we need to stand up against it and do everything possible to stop it.”

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